Reinforcement Learning for Finance

Chapter 9. Optimal Execution

Since the 2007–2008 crisis, Quantitative Finance has changed a lot. In addition to the classical topics of derivatives pricing, portfolio management, and risk management, a swath of new subfields has emerged, and a new generation of researchers is passionate about systemic risk, market impact modeling, counterparty risk, high-frequency trading, optimal execution, etc.

Guéant (2016)

Traditional finance theory often assumes that the actions of agents do not have any impact on markets or prices because they are so small compared to the group of all market participants. All applications in Part III so far fall into that category: no matter what the action of the agent is, the prices of the traded assets are not influenced.

In reality, however, trading relatively small quantities of shares of a stock can have an impact on the stock’s prices. This is even more the case when large blocks of shares are traded by large buy-side institutions, such as hedge funds, or large intermediaries, such as investment banks. The trade-off that traders face in such situations is between a fast execution that might have a large impact on prices and a slower execution that has a smaller impact on prices but leads to price risks due to the natural fluctuations in market prices.

By assumption, this trade-off is not present in Chapters 6–8. The typical assumption in models like that of Black-Scholes-Merton (1973) discussed in Chapter 7 is one of perfectly liquid markets or ...